Solve each absolute value inequality. Graph the solution:

The correct answer is: Combining the above two solutions, we get x ≤ - 10 and x ≥ 10

Step by step solution:
The given inequality is

2 ≤ |x| - 8
Adding 8 on both sides, we get

2 + 8 ≤ |x|
Finally, we get

|x |≥ 10
We use the definition of , which is

For, x < 0,
We have

|x| = - x ≥ 10
Multiplying  on both sides, we have

x ≤ - 10

Or

- 10 ≥ x
For, We have

|x| = x ≥ 10
That is

x ≥ 10
Combining the above two solutions, we get

x ≤ - 10 and x ≥ 10
We plot the above inequality on the real line.

The points -10 and 10 are included in the graph.

The given inequality contains only one variable. So, the graph is plotted on one dimension, which is the real line. Geometrically, the absolute value of a number may be considered as its distance from zero regardless of its direction. The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.